Related papers: Various Logistic Curves in SIS and SIR Models
Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…
This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to…
We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
Bayesian inference for statistical models with a hierarchical structure is often characterized by specification of priors for parameters at different levels of the hierarchy. When higher level parameters are functions of the lower level…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the…
Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by…
We have designed a computational model of a virus spread near the outbreak threshold. Using computer simulation we studied the Susceptible - Infected - Recovered (SIR) process where in consequence of a force of habit that is manifested by…
We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the…
The sequential importance sampling (SIS) algorithm has gained considerable popularity for its empirical success. One of its noted applications is to the binary contingency tables problem, an important problem in statistics, where the goal…
We provide general derivations of the partial slip boundary condition from microscopic dynamics and linearized fluctuating hydrodynamics. The derivations are based on the assumption of separation of scales between microscopic behavior, such…
The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the behaviour of symptomatic, asymptomatic and hospitalized patients of COVID-19 epidemic, including the effect of demographic…
We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed by individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local…
We try to justify rigorously, using a Wong-Zakai approximation argument, the susceptible-infected-susceptible (SIS) stochastic differential equation proposed in [2]. We discover that according to this approach the "right" stochastic model…
Sliced inverse regression (SIR) is a popular sufficient dimension reduction method that identifies a few linear transformations of the covariates without losing regression information with the response. In high-dimensional settings, SIR can…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…